X-rays have been used for imaging ever since the discovery thereof by Roentgen at the turn of the 19th century. Since available x-ray optics are severely limited, x-ray imaging is still mostly based on absorption shadow-graphs. This is basically true even for modern Computer Tomography (CT) imaging and, as a consequence, the brightness of the x-ray source is a figure of merit limiting both the exposure time and the attainable resolution in many applications.
Today x-ray imaging is a widespread and standard method in science, medicine and industry. Although well established, there are numerous applications that would greatly benefit from an increased brightness. Among these are applications in medicine requiring high spatial resolution, such as mammography and angiography, and emerging techniques requiring monochromatic radiation which currently can not be achieved with reasonable exposure times. Also, certain protein crystallography, today only possible at synchrotron radiation facilities, may be feasible with a compact source. Furthermore, a significant increase in the brightness of compact x-ray sources could enable phase imaging with reasonable exposure times. This is important since the phase contrast is often much higher than the absorption contrast. In addition, phase contrast imaging could reduce the absorbed dose during imaging.
The basic physics relied upon for x-ray production in compact electron-impact sources has been the same since the days of Roentgen. As the electrons impact the target they lose energy in one of two ways: either they can be decelerated in the electric field close to an atomic nucleus and emit continuous bremsstrahlung radiation, or they can knock out an inner-shell electron, resulting in the emission of a characteristic x-ray photon when the vacancy is filled. The efficiency of x-ray production by electron impact is very poor, typically below 1%, and the bulk of the energy carried by the electron beam is converted to heat.
The brightness of current state-of-the-art compact electron-impact x-ray sources is limited by thermal effects in the anode. The x-ray spectral brightness [i.e. photons/(mm2·sr·s·BW), where BW stands for bandwidth] is proportional to the effective electron-beam power density at the anode, which must be limited not to melt or otherwise damage the anode. Since the first cathode-ray tubes only two fundamental techniques, the line focus and the rotating anode, have been introduced to improve the power load capacity of the anode.
The line focus principle, introduced in the 1920s, utilizes the fact that the x-ray emission is non-Lambertian to increase the effective power load capacity by extending the targeted area but keeping the apparent source area almost constant by viewing the anode at an angle. Ignoring the Heel-effect and field of view, this trick increases the attainable power load capability by up to ˜10×. The rotating anode was introduced in the 1930s to further extend the effective electron-beam-heated area by rotating a cone-shaped anode to continuously provide a cool target surface.
After these improvements, progress with respect to brightness has been rather slow for compact electron-impact sources and has only been due to engineering perfection in terms of target material, heat conduction, heat storage, speed of rotation etc. Current state-of-the-art sources now allow for 100-150 kW/mm2 effective electron-beam power density. Typical high-end implementations are, e.g., 10 kW, 0.3×0.3 mm2 effective x-ray spot size angiography systems and 1.5 kW, 0.1×0.1 mm2 effective x-ray spot size fine-focus mammography systems. Low-power micro-focus sources (4 W, 5 μm effective x-ray spot diameter) have similar effective power densities (200 kW/mm2) and are also limited by thermal effects.
The power load limit of a modern rotating anode can be calculated by
                                          P                          A              effective                                =                                    π              ⁢                                                          ⁢                              l                ⁡                                  (                                                            T                      max                                        -                                          Δ                      ⁢                                                                                          ⁢                                              T                        margin                                                              -                                          T                      base                                                        )                                            ⁢                                                λρ                  ⁢                                                                          ⁢                                      c                    p                                    ⁢                  fR                  ⁢                                                                          ⁢                  δ                                                                    4              ⁢                                                          ⁢                                                δ                  2                                (                                  1                  +                                      k                    ⁢                                                                  tf                        ⁢                                                  δ                                                      π                            ⁢                                                                                                                  ⁢                            R                                                                                                                                              )                                                    ,                            (        1        )            where Aeffective is the apparent x-ray source area, R is the anode radius, l is the spot height, 2δ is the spot width, Tmax is the maximum permissible temperature before breakdown, ΔTmargin is a safety margin, Tbase is the anode starting temperature, λ is the thermal conductivity, ρ is the density, cp is the specific heat capacity, f is the rotation frequency, t is the load period, and k is a correction factor taking into account radial heat conduction, heat loss by radiation and anode thickness. As can be seen from Eq. 1, the only way to increase the power load limit is to increase the spot speed, i.e., f and R. Unfortunately even a quite unrealistic set of parameters (1 m diameter anode and 1 kHz rotation) would only increase the output flux ˜6×. It therefore seems unlikely that conventional x-ray source technology can be developed much further, even with significant engineering efforts.
A way to increase the brightness in compact electron-impact based hard-x-ray sources would be a fundamentally different anode configuration allowing a higher electron-beam power density. To this end, there has previously been reported a new liquid-metal-jet anode concept. This anode configuration could allow a significantly higher (>100×) thermal load per area than current state of the art due to fundamentally different thermal limitations, as explained below. Liquid-jet systems have been extensively used as targets in negligible-debris laser-produced plasma soft x-ray and EUV sources. A liquid-gallium jet has also been used as target in hard x-ray production in femto-second laser-plasma experiments. Furthermore, an electron beam has been combined with a water jet for low power soft x-ray generation via fluorescence. X-ray tubes with liquid anodes, either stationary or flowing over surfaces, have previously been reported but their advantages for high-brightness operation are limited due to the intrinsically low flow speed and cooling capacity of such systems. Recent work also includes a liquid anode flowing behind a thin window.
The much higher power-density capacity of liquid-metal-jet systems compared to conventional anodes (2-3 orders of magnitude or more) is, in brief, due to three main reasons: (i) different thermal properties of the liquid-jet anode compared to a solid anode, (ii) the potential for higher jet speeds than what is possible for a rotating anode, and (iii) the regenerative nature of the liquid jet, which makes the requirement of keeping the anode intact more relaxed.
However, when attempting to increase the power for such systems, emission of debris is a potential practical difficulty. Hence, improvements are called for to reduce the debris issue for liquid-jet anode x-ray sources.